using the method of prime factorization what is the L.C.M of 28,42, and 56

Question

use the prime factorization what is the L.C.M for 28,42,56

Answer 1

28=2*2*7

42=2*3*7

56=2*2*2*7

to be a multiple of 56 you need all of 56's prime factors

LCM=2*2*2*7 so far

to be a multiple of 42 you need only the 3 because you have the 2 and the 7

LCM=2*2*2*7*3 so far

you don't need anything from the factorization of 28 because you already have two 2's and a 7 and you want the least common multiple

LCM=2*2*2*7*3=168

LCM=168

 

if you want the GCF...

28=2*2*7

42=2*3*7

56=2*2*2*7

pick out all the prime factors that you see in all three factorizations

2 is common to all three

7 is common to all three

GCF=2*7=14

GCF=14

 

Answer 2

      28

    2   14

  2   2    7

 

28 = 2²(7)

 

         42

      2      21

    2    3      7

 

42 = 2(3)(7)

 

        56

     2     28

We already know factorization of 28.

 

56 = 2(2)(2)(7) = 2³(7)

 

we have:

2²(7)

2(3)(7)

2³(7)

 

To make them the same they each jeed the same 

factors.  The lowest power being the highest for

that factor in original numbers. 

three 2's, one 3, one 7

we need them all to be 2³(3)(7) = 56(3) = 168

 

LCM is 168